Related papers: Chaoticity in the vicinity of complex unstable per…
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem…
The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…
Spatio-temporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A…
A model, plane symmetric, 3-D potential, which preserves some features of galactic problems,is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry.…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
The morphology of the outer rings of early-type spiral galaxies is compared to integrations of massless collisionless particles initially in nearly circular orbits. Particles are perturbed by a quadrupolar gravitational potential…
As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
Cuspy triaxial potentials admit a large number of chaotic orbits, which moreover exhibit extreme "stickiness" that makes the process of chaotic mixing surprisingly inefficient. Environmental effects, modeled as noise and/or periodic…
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
We argue that inner rings in barred spiral galaxies are associated with specific 2D and 3D families of periodic orbits located just beyond the end of the bar. These are families located between the inner radial ultraharmonic 4:1 resonance…
The well-known bar instability of rotationally-supported disk galaxy models has been studied extensively since its first discovery over half a century ago. We were therefore very surprised to find cases of disks embedded in rigid halos,…
It is shown how the violation of the invariance of the $Z$-component of the orbital angular momentum $L_z$ in the axially symmetric potential of the Galaxy with a bar can serve as an indicator of the degree of orbital chaos of globular…
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading…
We summarize recent developments in the use of spectral methods for analyzing large numbers of orbits in N-body simulations to obtain insights into the global phase space structure of dark matter halos. The fundamental frequencies of…
We study the phase space of a particle moving in the gravitational field of a rotating black hole described by the Kerr metric from a geometrical perspective. In particular, we show the construction of a multidimensional generalization of…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
In the present article, we present a galactic gravitational model of three degrees of freedom, in order to investigate and reveal the behavior of orbits in a binary quasar system. The two quasars are hosted in a pair of interacting disk…